The price of a stock today is $$95$ and its volatility is $20\%.$ The risk$-$free rate is $3\%.$

Compute the price of a European call option with a strike of $$100$ and a maturity of $3$ months using the BSM model.

Compute the price of a European put option with a strike of $$100$ and a maturity of $3$ months.

Using the Vega, what is the new price of the call if the volatility decreases by $2\%.$

Using the Vega, what will be the price of a put if the volatility increases by $3\%.$

Using the delta, what will be the new call price if the underlying price increases by $$1\mathrm{.}5.$

Using the delta, what will be the price of the put is the underlying price decreases by $$2\mathrm{.}3.$